Reconsidering the origin of the 21 micron feature: Oxides in carbon-rich PPNe?

The origin of the so-called "21 micron" feature which is especially prominent in the spectra of some carbon-rich protoplanetary nebulae (PPNe}) is the matter of a lively debate. A large number of potential band carriers have been presented and discarded within the past decade. The present paper gives an overview of the problems related to the hitherto proposed feature identifications, including the recently suggested candidate carrier silicon carbide. We also discuss the case for spectroscopically promising oxides. SiC is shown to produce a strong resonance band at 20-21 micron if coated by a layer of silicon dioxide. At low temperatures, core-mantle particles composed of SiC and amorphous SiO$_2$ indeed have their strongest spectral signature at a position of 20.1 micron, which coincides with the position of the "21 micron" emission band. The optical constants of another candidate carrier that has been relatively neglected so far -- iron monoxide -- are proven to permit a fairly accurate reproduction of the "21 micron" feature profile as well, especially when low-temperature measurements of the infrared properties of FeO are taken into account. As candidate carrier of the "21 micron" emission band, FeO has the advantage of being stable against further oxidation and reduction only in a narrow range of chemical and physical conditions, coinciding with the fact that the feature, too, is detected in a small group of objects only. However, it is unclear how FeO should form or survive particularly in carbon-rich PPNe.Comment: 28 pages, 15 figures, accepted for publication in ApJ (December

Lyapunov spectra of billiards with cylindrical scatterers: comparison with many-particle systems

The dynamics of a system consisting of many spherical hard particles can be described as a single point particle moving in a high-dimensional space with fixed hypercylindrical scatterers with specific orientations and positions. In this paper, the similarities in the Lyapunov exponents are investigated between systems of many particles and high-dimensional billiards with cylindrical scatterers which have isotropically distributed orientations and homogeneously distributed positions. The dynamics of the isotropic billiard are calculated using a Monte-Carlo simulation, and a reorthogonalization process is used to find the Lyapunov exponents. The results are compared to numerical results for systems of many hard particles as well as the analytical results for the high-dimensional Lorentz gas. The smallest three-quarters of the positive exponents behave more like the exponents of hard-disk systems than the exponents of the Lorentz gas. This similarity shows that the hard-disk systems may be approximated by a spatially homogeneous and isotropic system of scatterers for a calculation of the smaller Lyapunov exponents, apart from the exponent associated with localization. The method of the partial stretching factor is used to calculate these exponents analytically, with results that compare well with simulation results of hard disks and hard spheres.Comment: Submitted to PR

Goldstone modes in Lyapunov spectra of hard sphere systems

In this paper, we demonstrate how the Lyapunov exponents close to zero of a system of many hard spheres can be described as Goldstone modes, by using a Boltzmann type of approach. At low densities, the correct form is found for the wave number dependence of the exponents as well as for the corresponding eigenvectors in tangent-space. The predicted values for the Lyapunov exponents belonging to the transverse mode are within a few percent of the values found in recent simulations, the propagation velocity for the longitudinal mode is within 1%, but the value for the Lyapunov exponent belonging to the longitudinal mode deviates from the simulations by 30%. For higher densities, the predicted values deviate more from the values calculated in the simulations. These deviations may be due to contributions from ring collisions and similar terms, which, even at low densities, can contribute to the leading order.Comment: 12 pages revtex, 5 figures, accepted by Physical Review

The Lyapunov spectrum of the many-dimensional dilute random Lorentz gas

For a better understanding of the chaotic behavior of systems of many moving particles it is useful to look at other systems with many degrees of freedom. An interesting example is the high-dimensional Lorentz gas, which, just like a system of moving hard spheres, may be interpreted as a dynamical system consisting of a point particle in a high-dimensional phase space, moving among fixed scatterers. In this paper, we calculate the full spectrum of Lyapunov exponents for the dilute random Lorentz gas in an arbitrary number of dimensions. We find that the spectrum becomes flatter with increasing dimensionality. Furthermore, for fixed collision frequency the separation between the largest Lyapunov exponent and the second largest one increases logarithmically with dimensionality, whereas the separations between Lyapunov exponents of given indices not involving the largest one, go to fixed limits.Comment: 8 pages, revtex, 6 figures, submitted to Physical Review

Dusty shells surrounding the carbon variables S Scuti and RT Capricorni

For the Mass-loss of Evolved StarS (MESS) programme, the unprecedented spatial resolution of the PACS photometer on board the Herschel space observatory was employed to map the dusty environments of asymptotic giant branch (AGB) and red supergiant (RSG) stars. Among the morphologically heterogeneous sample, a small fraction of targets is enclosed by spherically symmetric detached envelopes. Based on observations in the 70 {\mu}m and 160 {\mu}m wavelength bands, we investigated the surroundings of the two carbon semiregular variables S Sct and RT Cap, which both show evidence for a history of highly variable mass-loss. S Sct exhibits a bright, spherically symmetric detached shell, 138" in diameter and co-spatial with an already known CO structure. Moreover, weak emission is detected at the outskirts, where the morphology seems indicative of a mild shaping by interaction of the wind with the interstellar medium, which is also supported by the stellar space motion. Two shells are found around RT Cap that were not known so far in either dust emission or from molecular line observations. The inner shell with a diameter of 188" shows an almost immaculate spherical symmetry, while the outer ~5' structure is more irregularly shaped. MoD, a modification of the DUSTY radiative transfer code, was used to model the detached shells. Dust temperatures, shell dust masses, and mass-loss rates are derived for both targets

Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering

In recent work a deterministic and time-reversible boundary thermostat called thermostating by deterministic scattering has been introduced for the periodic Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the nonlinear properties of this new dynamical system by numerically calculating its Lyapunov exponents. Based on a revised method for computing Lyapunov exponents, which employs periodic orthonormalization with a constraint, we present results for the Lyapunov exponents and related quantities in equilibrium and nonequilibrium. Finally, we check whether we obtain the same relations between quantities characterizing the microscopic chaotic dynamics and quantities characterizing macroscopic transport as obtained for conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript

A discretized integral hydrodynamics

Using an interpolant form for the gradient of a function of position, we write an integral version of the conservation equations for a fluid. In the appropriate limit, these become the usual conservation laws of mass, momentum and energy. We also discuss the special cases of the Navier-Stokes equations for viscous flow and the Fourier law for thermal conduction in the presence of hydrodynamic fluctuations. By means of a discretization procedure, we show how these equations can give rise to the so-called "particle dynamics" of Smoothed Particle Hydrodynamics and Dissipative Particle Dynamics.Comment: 10 pages, RevTex, submitted to Phys. Rev.

Impact of excess NOx emissions from diesel cars on air quality, public health and eutrophication in Europe

Diesel cars have been emitting four to seven times more NOx in on-road driving than in type approval tests. These ‘excess emissions’ are a consequence of deliberate design of the vehicle’s after-treatment system, as investigations during the ‘Dieselgate’ scandal have revealed. Here we calculate health and environmental impacts of these excess NOx emissions in all European countries for the year 2013. We use national emissions reported officially under the UNECE Convention for Long-range Transport of Atmospheric Pollutants and employ the EMEP MSC-W Chemistry Transport Model and the GAINS Integrated Assessment Model to determine atmospheric concentrations and resulting impacts. We compare with impacts from hypothetical emissions where light duty diesel vehicles are assumed to emit only as much as their respective type approval limit value or as little as petrol cars of the same age. Excess NO2 concentrations can also have direct health impacts, but these overlap with the impacts from particulate matter (PM) and are not included here. We estimate that almost 10 000 premature deaths from PM2.5 and ozone in the adult population (age >30 years) can be attributed to the NOx emissions from diesel cars and light commercial vehicles in EU28 plus Norway and Switzerland in 2013. About 50% of these could have been avoided if diesel limits had been achieved also in on-road driving; and had diesel cars emitted as little NOx as petrol cars, 80% of these premature deaths could have been avoided. Ecosystem eutrophication impacts (critical load exceedances) from the same diesel vehicles would also have been reduced at similar rates as for the health effects